The web monoid and opetopic sets

We propose a new approach to opetopic sets. It is based on fibrations and the web monoid, which plays a role analogous to the operad for operads of Baez and Dolan and the multicategory of function replacement of Hermida, Makkai and Power. In contrast to its two predecessors, the web monoid is a completely abstract construction available in any fibration with the requisite structure. In this paper we define that additional structure and prove that the web monoid (characterized by certain natural properties) exists and is unique. This allows us to give a new definition of opetopic sets.